Jordan, C. R. and Jordan, D. A.
(1976).
*Communications in Algebra*, 4(7) pp. 647–656.

DOI (Digital Object Identifier) Link: | https://doi.org/10.1080/00927877608822125 |
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Google Scholar: | Look up in Google Scholar |

## Abstract

A well known result on polynomial rings states that, for a given ring , if has no non-zero nil ideals then the polynomial ring (x) is semiprimitive, see for example (5) p.12. In this note we study Ore extensions of the form (x,δ), where δ is an automorphism on the ring , with the aim of relating the question of the semiprimitivity of (x,δ) to the presence of non-zero nil ideals in . In particular we show that under certain chain conditions the Jacobson radical of (x,δ) consists precisely of polynomials over the nilpotent radical of . Without restriction on we show that if δ has finite order then (x,δ) is semiprimitive if has no nil ideals. Some conditions are required on and δ for results of the above nature to be true, as illustrated in §5 by an example of a semiprimitive ring having an automorphism δ of infinite order such that (x,δ) has nil ideals.

Item Type: | Journal Item |
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Copyright Holders: | 1976 Marcel Dekker |

ISSN: | 1532-4125 |

Extra Information: | MR number MR0404314 |

Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 31530 |

Depositing User: | Camilla Jordan |

Date Deposited: | 09 Feb 2012 11:37 |

Last Modified: | 07 Dec 2018 10:00 |

URI: | http://oro.open.ac.uk/id/eprint/31530 |

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